You'd also need a new crown and most manufacturers aren't keen on reusing your stanchions either. So you'd really need what's called a "CSU" - which is a fresh crown, steerer, and stanchions (uppers). That'll cost you at least $300 at retail - a costly endeavor.

However, it is possible on some frames to fit a tapered steerer in a head-tube originally designed for a straight steerer. If you're frame uses an 1-1/8" zero stack lower headset, there are conversion headsets now available from Cane Creek and others to externalize your headset and fit a tapered steerer. This only works on Zero Stack headsets with pressed-in cups, not the IS style where the bearing sits directly in the frame.

It will void your warranty and possibly your life, but I have replaced two steertubes in forks. I used 7000 series aluminum and a healthy amount of press fit. One was on a Manitou Super Nova single crown. The other was a bit safer as it was on a Dorado triple clamp. Neither one has given me any problems. I don't recommend it, but it can be done.